Parts (a) and (b) in Assumption REF  are standard unbiasedness and bounded variance assumptions on the stochastic gradient, common in the literature. Part (c) is essential to establish the convergence results in the multi-level case. Similar assumptions have been made, for example, in [1]} and [2]}. We also emphasize that unlike some prior works (see e.g., [3]}), Assumption REF  allows the case of endogenous uncertainty, and we do not require the distribution of the random variables \((\xi _i)_{1\le i \le T}\)  to be independent of the distribution of the decision variables \((u_i)_{1\le i \le T}\) .
